Probability and Statistics: math test solutions, Grade 11 – download the PDF

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7 October 20267 October 2026

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Test solutions Grade 11 : Probability and Statistics — Zyro the alien explorer of Planète Maths

Test solutions with the detailed point scale. Add up your points and spot what to review.

Suggested time: 45 minutes. Out of 20 points. Calculator allowed only when the problem says so.

Sommaire

1 Counting / 3 pts

(a) Order matters: \(P(9,3)=9\times8\times7=504\). (1 pt)

(b) Order does not matter: \(C(9,3)=\dfrac{504}{6}=84\). (1 pt)

2 Marbles / 4 pts

(a) \(\dfrac5{10}\times\dfrac49=\dfrac{20}{90}=\dfrac29\). (1.5 pts)

(b) Red: \(\dfrac{20}{90}\). Blue: \(\dfrac3{10}\times\dfrac29=\dfrac6{90}\). Yellow: \(\dfrac2{10}\times\dfrac19=\dfrac2{90}\). Sum: \(\dfrac{28}{90}=\dfrac{14}{45}\). (1.5 pts)

3 Conditional probability / 3 pts

(a) \(\dfrac{36}{80}=0.45\). (1 pt)

(b) There are \(36+42=78\) purchases: \(\dfrac{36}{78}=\dfrac6{13}\approx0.462\). (1 pt)

4 Binomial model / 3 pts

(a) \(C(6,5)(0.9)^5(0.1)=6\times0.59049\times0.1\approx0.3543\). (1 pt)

(b) Add \(P(X=6)=0.9^6\approx0.5314\): total \(\approx0.8857\). (1 pt)

5 Watermelons / 4 pts

(a) \(z=\dfrac{15-12}{1.5}=2\) (1 pt) and \(z=\dfrac{10.5-12}{1.5}=-1\). (1 pt)

(b) 9 and 15 are \(\mu\pm2\sigma\): about 95%. (1 pt)

6 Poll and bias / 3 pts

(a) \(ME=1.96\sqrt{\dfrac{0.54\times0.46}{900}}\approx1.96\times0.0166\approx0.033\), about 3.3%. (1 pt)

(b) The interval is about 50.7% to 57.3%. It lies entirely above 50%, so a majority is supported at the 95% level. (1 pt)

(c) It is a convenience sample: gym users are not representative of the whole population, so the result is biased no matter how many people answer. (1 pt)